There are many instruments available for measuring the volume flow rate of a fluid (in liters/sec, for example). But for many applications, such as jet engine control, it is necessary to have an instrument which can accurately measure the mass flow rate (in Kg/sec, for example). The volume flow rate can be converted to mass flow rate if the density (in Kg/liter, for example) of the fluid is known. However, the density of the fluid depends on the temperature of the fluid and its composition which are often not known with the accuracy required to convert volume flow rate to mass flow rate.
U.S. Pat. No. 3,132,512 ("Roth") describes a gyroscopic mass flowmeter that operates on the principle of Coriolis forces and, in theory, is capable of measuring true mass flow rate. The mass flowmeter is basically a circular tube that is excited to vibrate in a direction normal to the plane in which it is at rest. The fluid whose mass flow rate is to be measured is made to flow through the tube. The Coriolis force on the tube resulting from the combined fluid flow and vibration causes the tube to twist. For a given geometry and vibration, the angle of twist of the tube is proportional to the true mass flow rate. The angle of twist can be determined by measuring the time difference between the instant that one side of the tube crosses a given reference plane and the instant that the opposite side crosses the same reference plane.
It is not necessary for the tube to be circular; a U-shaped tube may also be used. Mass flowmeters or mass-flow sensors using this principle are manufactured by Micro-Motion of Boulder, Colorado. The Micro-Motion instrument uses two U-shaped tubes that vibrate in opposite directions, in the manner of a tuning fork. Devices using two U-shaped tubes are described in U.S. Pat. No. 4,127,028 ("Cox, et al.") and in U.S. Pat. No. 4,252,028 ("Smith, et al.").
An instrument based on the Roth patent, or the later patents, however, behaves as a gyroscope when the base of the instrument accelerates or rotates in space. This type of motion could occur, for example, in a maneuvering aircraft. The gyroscopic behavior in the rotational environment can produce error signals that may, under certain circumstances, be nearly as large as the signals produced by the true mass flow.